Operations Research
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic inference and influence diagrams
Operations Research
Valuation-based systems for Bayesian decision analysis
Operations Research
Approximating probabilistic inference in Bayesian belief networks is NP-hard
Artificial Intelligence
Approximating MAPs for belief networks is NP-hard and other theorems
Artificial Intelligence
Probabilistic Expert Systems
Computational Properties of Two Exact Algorithms for Bayesian Networks
Applied Intelligence
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Use of Elvira's explanation facility for debugging probabilistic expert systems
Knowledge-Based Systems
On the classification performance of TAN and general Bayesian networks
Knowledge-Based Systems
Exploiting contextual independence in probabilistic inference
Journal of Artificial Intelligence Research
Dynamic local search for the maximum clique problem
Journal of Artificial Intelligence Research
Query DAGs: a practical paradigm for implementing belief-network inference
Journal of Artificial Intelligence Research
Improvements to message computation in lazy propagation
International Journal of Approximate Reasoning
Understanding the scalability of Bayesian network inference using clique tree growth curves
Artificial Intelligence
Symbolic probabilistic inference in belief networks
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Any-space probabilistic inference
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Bucket elimination: a unifying framework for probabilistic inference
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Value elimination: bayesian inference via backtracking search
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
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Inference in Bayesian networks (BNs) is NP-hard. We proposed the concept of a node set namely Maximum Quadruple-Constrained subset MQC(A,a-e) to improve the efficiency of exact inference in diagnostic Bayesian networks (DBNs). Here, A denotes a node set in a DBN and a-e represent five real numbers. The improvement in efficiency is achieved by computation sharing. That is, we divide inference in a DBN into the computation of eliminating MQC(A,a-e) and the subsequent computation. For certain complex DBNs and (A,a-e), the former computation covers a major part of the whole computation, and the latter one is highly efficient after sharing the former computation. Searching for MQC(A,a-e) is a combinatorial optimization problem. A backtracking-based exact algorithm Backtracking-Search (BS) was proposed, however the time complexity of BS is O(n^32^n) (n=|A|). In this article, we propose the following algorithms for searching for MQC(A,a-e) especially in complex DBNs where |A| is large. (i) A divide-and-conquer algorithm Divide-and-Conquer (DC) for dividing the problem of searching for MQC(A,a-e) into sub-problems of searching for MQC(B"1, a-e),...,MQC(B"m,a-e), where B"i@?A(1=